Browning did make and sell some guns in the beginning. He and his brothers built and sold about 600 single shot rifles before selling the patent to Winchester. When Winchester and Browning couldn't come to terms on the automatic shotgun, John Browning went to Belgium with the design. FN was already building several pistols under Browning's patents and jumped at the chance to build the automatic shotgun. Browning built them under the FN name for sale in Europe, and Remington and Savage built them under license in the US. FN built the guns that were imported to the US by the Browning Arms Co. before and after WWII.
During WWII, Remington built guns under the Browning name until Browning got back in production in Belgium.